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$$C^1$$ connecting lemmas. (English) Zbl 0947.37018
Summary: Like the closing lemma, the connecting lemma is of fundamental importance in dynamical systems. Hayashi recently proved the $$C^1$$ connecting lemma for stable and unstable manifolds of a hyperbolic invariant set. In this paper, we prove several very general $$C^1$$ connecting lemmas. We simplify Hayashi’s proof and extend the results to more general cases.

##### MSC:
 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37C75 Stability theory for smooth dynamical systems
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##### References:
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